Spectral gaps of Schrödinger operators with periodic singular potentials

Abstract

By using quasi--derivatives we develop a Fourier method for studying the spectral gaps of one dimensional Schrödinger operators with periodic singular potentials $v.$ Our results reveal a close relationship between smoothness of potentials and spectral gap asymptotics under a priori assumption $v\in H_{loc}^{-1}(\mathbb{R}).$ They extend and strengthen similar results proved in the classical case $v\in L_{loc}^2(\mathbb{R}).$

References in corpus (3)

• Inverse spectral problems for Sturm-Liouville operators with singular potentials
• A priori estimates for the Hill and Dirac operators
• Deviations of Riesz projections of Hill operators with singular potentials

Cited by in corpus (2)

• Weyl-Titchmarsh Theory for Sturm-Liouville Operators with Distributional Potentials
• Irreducibility of some spectral determinants